Another difficulty created by the possible overlaps in the IFSs comes from the zooming-in operation of \(\theta ^+_{t,\mathbf {i}^-,\mathbf {j}^-}\)  on \(\Sigma _a^+\times \Sigma _b^+\)  according to \(\Phi \) . To capture the dynamics of the zooming-in procedure for \(\Phi (\theta ^+_{t,\mathbf {i}^-,\mathbf {j}^-})\) , one needs to use a family of rectangles \(\mathcal {U}\)  (see (REF ) for definition) instead of balls on the Euclidean space. This creates problems when applying the dominated convergence result of conditional informations ([1]}), as in there the differentiation theory of measures, Besicovitch covering lemma and Hardy-Littlewood maximal inequality are all applied in terms of balls. Fortunately we have a complete analogue of these theorems in terms of the so-called \(\gamma \) -Morse sets, which covers our family \(\mathcal {U}\)  of rectangles. See [2]} and Section REF .
